Half a dozen Coalition MPs have told Prime Minister Scott Morrison they will cross the floor on a call for the government to establish a royal commission on veteran suicides, as legislation for the government’s preferred option of an ongoing national commissioner remains stalled in the Senate.

A motion noting veterans have a suicide rate twice that of the general population and calling for a royal commission to examine the problem and solutions passed the Senate on Thursday with the backing of Labor, the Greens, One Nation and independents Jacqui Lambie and Rex Patrick. It will head to the House of Representatives for concurrence next week.

Veterans among the government’s ranks told Mr Morrison they would cross the floor on the motion if it came to a vote, a source involved in the discussion who spoke on the condition of anonymity said. At least one was told the Prime Minister would not pressure them, and the motion is expected to pass without a division, meaning the names of supporters won’t be recorded.

After Craig Kelly quit the Liberal Party in February to sit as an independent, the government only holds 75 seats in the 151-seat lower house, with Speaker Tony Smith acting as the casting vote in the event of a tie.

Mr Kelly supports the push for a royal commission, as does independent MP Bob Katter.

Labor’s veteran’s affairs spokesman Shayne Neumann said: “the Prime Minister’s got no alternative” to letting the motion through.

Former SAS major Heston Russell, who has been campaigning for a royal commission, said he understood there were six MPs who had been considering crossing the floor and others looking at abstaining.

“A lot of these people have actually gone to the Prime Minister saying it’s a bit of a no-brainer, we only have everything to gain from supporting this, this conversation’s gone on for too long, can we please just call it before it goes to a vote,” he said.