Democratic Unionist Party (DUP) leader Gavin Robinson has said he is "very sorry" that MP Carla Lockhart has quit the party.

Robinson said he would not be criticising the Upper Bann MP, who left the party on Monday over its response to the Drumcree parading dispute and expressed hope they would continue to work together in the future.

Lockhart had been calling for the DUP to withdraw Stormont's deputy first minister to force Sinn Féin First Minister Michelle O'Neill from their joint office.

Speaking on Tuesday, Robinson said the disagreement was over strategy not sentiment Analysis: Lockhart departure presents massive challenge for DUP and unionism O'Neill and several other senior Sinn Féin figures have been interviewed by police investigating the Garvaghy Road demonstrations, with unionists accusing the party of acting unlawfully.

Last week the DUP, which shares power with Sinn Féin in Northern Ireland's devolved government, announced it would block official engagements involving O'Neill in response to the fall-out. But Robinson stopped short of Lockhart's call to force O'Neill from office.

Speaking on the Good Morning Ulster programme he said: "We share exactly the same sentiment - all of us are angered, all of us believe the position of Michelle O'Neill and her willingness to break the law, to ignore the courts, to breach her pledge of office requires sanction.

"So while we share the same sentiment, we have not been in agreement when it comes to how you deal with it.

"The Democratic Unionist Party is firmly of the view that it is Michelle O'Neill who should face the consequences of her actions, not the rest of the people of Northern Ireland.

"Northern Ireland needs a functioning government, Northern Ireland needs a budget - those important discussions will continue on Thursday I believe with the secretary of state." Robinson said he believes "there is a role for this government to come forward with a sanctions regime that will punish those who break the pledge of office".

Speaking after a meeting of the Northern Ireland Executive, Deputy First Minister Emma Little-Pengelly reiterated DUP calls for "unionist cooperation" and warned that unionism was "weakened by infighting".

Little-Pengelly said the unionist community felt "anger and frustration" over Sinn Féin's response to Drumcree and the Irish republican party had "fractured" relations within Northern Ireland's power-sharing government.

O'Neill, the Sinn Féin vice-president, has defended her involvement in the Drumcree protests, saying it was the "right thing to do".

In an open letter to colleagues last week, Lockhart said forcing O'Neill from office was the "only one credible option" and any kind of "graduated response" would be "insulting to those who have trusted us".

In a statement posted on her Facebook page on Monday, the MP said: "My first responsibility remains to the people of Upper Bann.

"You placed your trust in me, and I will continue to work every bit as hard for you, your family and our community." Lockhart said she was leaving the DUP on a "point of principle" and would continue in the House of Commons as an independent unionist.

"I cannot stand idly by whilst Sinn Féin wilfully ignores the rule of law and the promised profound consequences fail to materialise," she added.

Lockhart concluded that she would "look forward to working with all shades of unionism, elected or not, to advance the cause we love".

On Tuesday, Lockhart told UTV News that she bears no animosity towards Robinson, but added that "people are ahead of where political parties are", including the DUP, "on this issue". A local councillor has also quit the party.

Clement Cuthbertson, a councillor for Dungannon in Mid Ulster District Council, has been a DUP member for 30 years and will continue his elected role on the council as an independent unionist.

"I have reached the point where remaining a party member would mean asking people to accept a position I cannot defend," he said in a social media post.

A DUP spokesperson said: "We regret Clement Cuthbertson's decision to resign from the party and wish him well for the future." The DUP MP for East Londonderry Gregory Campbell said Lockhart's resignation had come as no surprise and could prove a "pivotal moment" for the wider unionist family.

"Do we advance the cause of unionism by fracturing or closing ranks and uniting and trying to get people together to say 'what is the best way forward, what's the best way to set out a strategy what will maximise the pro-union voice?'," he told BBC Radio Foyle's North West Today programme.

"Fracturing only assists those who are the enemies of unionism, uniting will thwart the enemies of unionism and that's what we need to do and I think that realisation is going to come home now in the next few weeks." Speaking on the Good Morning Ulster programme on Tuesday, Traditional Unionist Voice leader Jim Allister said the DUP had "preferred to keep Michelle O'Neill and let Carla Lockhart go" and that would "hang over them and haunt them for some time to come".

He added: "I have both publicly and privately made it very plain that Carla would be very welcome in the TUV, but I understand Carla's position.

"When you've been in a party as she has and indeed as I was for 20 years and then you leave it, it's quite a step." Also on Tuesday, Sinn Féin Finance Minister John O'Dowd said the DUP needs to "set party politics aside" as the executive works to agree a budget.

He was speaking after ministers met ahead of further talks with the secretary of state later this week.

O'Dowd said all ministers need to remain focused on the task at hand, and that he will present further options to them about what is possible in the coming days.

There is the prospect of strike action by health workers if they do not get a long-awaited pay deal that cannot be released without a budget.

O'Dowd said the primary task was to ensure strikes are avoided, adding: "We are reaching a crunch period in relation to the discussions around the executive table and the terms and conditions with the British government." On the absence of a Stormont budget and further talks this week with the secretary of state, Little-Pengelly said that "we are in a better position than where we were" but there was "still a significant gap".