More than 200 US mayors earlier wrote to McConnell to demand that the chamber reconvene to approve bills passed by the lower House requiring background checks for all gun purchases and regulation of secondary sales after the shootings in El Paso and Dayton.

But McConnell told local radio in Kentucky that while gun legislation would be "front and center" in the Senate's next session, he would not order the recall and instead wanted to wait for "bipartisan discussion" between Republicans and Democrats.

"I want to make a law, not just see this political sparring going on endlessly," he told NewsRadio 840 WHAS, adding that a possible ban on assault weapons would "probably be discussed as well" when lawmakers returned in September.

McConnell has stifled congressional efforts to expand gun controls amid Republicans' fears that they could suffer at ballot box in next year's elections.

Thursday's letter from the influential US Conference of Mayors pointed to two background check bills passed by the Democrat-controlled House in February that McConnell has essentially blocked from consideration in the Republican-controlled Senate.

On Wednesday President Donald Trump said he supported proposed legislation in the Senate that would block gun sales to people with mental health issues.

But Trump said he did not think there was political support for tougher legislation, like that passed already by the House, or bans on highly lethal assault rifles used in many mass shootings