Speaking in Connecticut where 26 people died in Sandy Hook massacre last year, President Barack Obama said citizens must demand action.
Opinion polls have shown a majority of Americans support a ban on assault weapons and other gun control measures.
But gun rights groups, including the National Rifle Association (NRA), have been lobbying politicians against the bill.
“The day Newtown happened was the toughest day of my presidency,” Barack Obama said in his speech at Hartford, not far from Newtown, scene of the mass shooting four months ago.
“But I’ve got to tell you, if we don’t respond to this, that’ll be a tough day for me too.”
The Associated Press news agency reports there were tears in Barack Obama’s eyes as he described Newtown parent Nicole Hockley, who has said every night she asks her 6-year-old son Dylan to come to her in her dreams so she can see him again.
“If there’s even one thing we can do to prevent a father from having to bury his child, isn’t that worth fighting for?” Barack Obama asked, amid repeated standing ovations from the crowd.
He called for a vote on his three gun legislation priorities – strengthening background checks on gun buyers, limiting the size of ammunition magazines to 10 rounds, and a ban on assault weapons.
However, the US Senate recently ditched the proposed ban on assault weapons and on high-capacity magazines, saying there was not enough support for the measure.
On Monday, Barack Obama said curbing gun violence was more important than partisan politics.
“Connecticut, this is not about me,” he said.
“This is not about politics.
“This is about doing the right thing for all the families who are here that have been torn apart by gun violence.”
Eleven parents of young children who were killed in the Newtown school shooting returned to Washington DC with Barack Obama aboard his official plane, Air Force One.
They are due to lobby members of Congress who have not yet backed the gun control bill.
Barack Obama said: “Nothing’s going to be more important in making sure that the Congress moves forward this week than hearing from them.”
The president criticized Republicans who have threatened to use a procedural tactic known as a filibuster to delay a vote on the gun bill.
Thirteen senators have said in a letter to Senate Majority Leader Harry Reid they would take such action, after he brought the bill to the Senate floor for debate on Monday.
“Some back in Washington are already floating the idea that they may use political stunts to prevent votes on any of these reforms. Think about that,” said Barack Obama.
“They’re not just saying they’ll vote <<no>> on ideas that almost all Americans support.
“They’re saying they’ll do everything they can to even prevent any votes on these provisions. They’re saying your opinion doesn’t matter. And that’s not right.”
Barack Obama’s speech came a week after Connecticut Governor Dannel Malloy signed sweeping gun-control measures into law.
Connecticut follows the states of Colorado and New York in passing tighter state gun laws.
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