(Reuters) - President Donald Trump wants to keep discussing tougher background checks for gun purchases, a leading Democratic senator on gun control said on Friday, adding that Trump’s support is crucial for the U.S. Congress to pass reform legislation when it returns to work next month.

Connecticut Senator Chris Murphy, who sponsored a background-checks bill intended to prevent mass shootings like those that recently killed 31 people in Texas and Ohio, said the White House reassured him the Republican president wants to move forward. Murphy said the White House also confirmed its interest in “red flag laws” that temporarily keep guns away from potentially violent people.

“Several days ago some of the president’s comments seemed to suggest that he was once again backing away from his commitment to work on background checks legislation,” Murphy said at a briefing in Connecticut. “I have been in contact with the White House this week since the president’s comments - as late as last night - and I believe that the White House is still committed to trying to work on a comprehensive anti-gun violence proposal that would include strengthening background checks.”

But Murphy sounded a downbeat note. The White House is difficult to negotiate with and Trump has buckled in the past on pledges to tighten gun controls under pressure from lobby groups such as the National Rife Association, Murphy said.

Without Trump’s support any measures would die in the Republican-dominated Senate, Murphy said.

“The president’s language is always vague and hard to follow on almost every issue he talks about and it has been especially difficult to parse when he’s talking about the issue of changing America’s gun laws,” Murphy said. “He’s talking to the gun lobby much more frequently than he’s talking to me.”

Trump has rejected accusations from Democrats, who control the House of Representatives, that he is backing down on background checks. On Wednesday, he said he spoke with the NRA about closing loopholes in background checks but he did not want to take away the constitutional right to own guns.