At the daily Downing Street news conference, Mr Williamson said his "door is always open", as he warned it was the most disadvantaged pupils who would suffer the most, the longer schools remained closed.
His plea came amid fears that plans to start the phased re-opening of primary schools from next month, as part of the easing of the coronavirus lockdown in England, may be scuppered if the unions refuse to co-operate.
Talks on Friday between union representatives and government scientific advisers, intended to provide assurance about the Government's proposals to enable children to return safely, ended inconclusively.
Leeds: Post-school learning for those with additional needs
Secondary schools in Leeds: the seven best secondary schools in Leeds according to Government data
The top 30 UK universities for research have been revealed - including one in Leeds
The Class of 2022 celebrate success at Leeds Trinity
Progressions Leeds has a fantastic range of courses
Union leaders said afterwards that the discussions had raised more questions than answers.
At the news conference, Mr Williamson went out of his way to lavish praise on teachers, saying they had been "absolute heroes" during the coronavirus crisis, while urging them to talk.
"My door is always open. I am always keen to listen and talk to them. I have been meeting both representative organisations, school groups, but also unions, every single week," he said.
"I always want to talk. We want to find practical solutions to make sure that those children from that most disadvantaged background don't lose out as a result of this crisis.
"I hope everyone is unified in that mission to deliver that."
Earlier, Patrick Roach, general secretary of the NASUWT teaching union, said they needed to see "unequivocal guidance" from the Government that schools could be made "Covid secure" and re-opening would not put public health at risk.
"We are continuing to say to Government, but also to schools and employers, that we are here, we want to work with those employers to put plans in place to see whether schools can be ready for re-opening from June 1," he told the BBC Radio 4 Today programme.
"We want schools to be re-opened, we want children to be safe and we want staff to be safe.
"It is not a zero sum game here. It is about ensuring that we get back to a place where we can return to some form of normality."