A bipartisan group of US senators on Sunday proposed steps to curb gun violence following devastating mass shootings in Texas and New York, but the limited measures fall far short of the president's calls for change.

The proposals include tougher background checks for gun buyers under 21, increasing resources for states to keep weapons out of the hands of people deemed a risk, and cracking down on illegal gun purchases.

"Today, we are announcing a commonsense, bipartisan proposal to protect America’s children, keep our schools safe, and reduce the threat of violence across our country," the group of 20 Democratic and Republican lawmakers said in a statement.

"Our plan increases needed mental health resources, improves school safety and support for students, and helps ensure dangerous criminals and those who are adjudicated as mentally ill can't purchase weapons," they said.

The senators also called for increased investment in mental health services and school safety resources, as well as including domestic violence convictions and restraining orders in the national background check database.

President Joe Biden praised the announcement and urged lawmakers to pass it quickly, while making clear that the proposals do not go as far as he wanted.

"Obviously, it does not do everything that I think is needed, but it reflects important steps in the right direction, and would be the most significant gun safety legislation to pass Congress in decades," he said in a statement.

"With bipartisan support, there are no excuses for delay, and no reason why it should not quickly move through the Senate and the House."

The president had pushed for far more substantive reforms, including a ban on assault rifles -- which were used in shootings at a Texas elementary school that killed 21 people and a New York State supermarket that left 10 dead -- or at least an increase in the age at which they can be purchased.

He had also urged lawmakers to strengthen background checks, mandate safe storage of firearms, and allow gun manufacturers to be held liable for crimes committed with their products.

The Democrat-controlled House of Representatives passed a broad package of proposals that included raising the purchasing age for most semi-automatic rifles from 18 to 21.

But the party does not have the requisite 60 votes to advance it in the Senate, leaving the bipartisan deal as the only hope for federal measures to address firearms violence.