The meeting is the latest in a series between Mr Abbott and the incoming senator crossbench, most of whom are expected to back the government's long-held desire to repeal the carbon and mining, taxes but who could block billions of savings outlined in the budget.

Senator Lambie has also accused Mr Abbott of "parading his daughters around" during the election campaign, potentially risking their personal security.

The meeting took place before Senator Lambie was formally sworn into her role along with other senators, including 11 new arrivals. Liberal Senator Stephen Parry was voted in as Senate president in a secret ballot.

Mr Abbott and Senator Lambie met for about 30 minutes and discussed areas of concern to the Tasmanian senator, including the needs of her home state, veterans and defence issues.

A spokeswoman for the Prime Minister said the meeting was a chance for the pair to compare notes on issues of concern to Senator Lambie.

Mr Abbott has held meetings with Motoring Enthusiast senator Ricky Muir, Palmer United leader Clive Palmer, Family First senator Bob Day, Liberal Democratic senator David Leyonhjelm, Democratic Labor Party senator John Madigan and independent Nick Xenophon.

He is expected to meet Palmer senators Glenn Lazarus and Dio Wang in the coming weeks.

The new senate is sitting for the first time on Monday, with senators being sworn in and Tasmanian Liberal senator Stephen Parry to be named the chamber's new president.

Beginning the process of repealing the carbon tax will be the first order of business for the new senate.

Labor Senate leader Penny Wong said the government should wait until a Senate committee report into the carbon price repeal is delivered on July 14 before reintroducing legislation to scrap it.

Ms Wong said the government was rushing the new crossbenchers to score a "political win".

On being described by Senator Lambie as one of her political heroes, Ms Wong told ABC radio: "It's very kind of her. I was going to say to Jacqui when I see her in person: it's not often I'm on the same list as Margaret Thatcher. Women in politics, as we know, have to hold their own and I think Jacqui demonstrates her capacity to do that and good on her."

Just three of those taking their seats on the red benches for the first time ran the media gauntlet outside Parliament House on Monday.

Senator Leyonhjelm told reporters that his new role, ''scares the crap out of me''.

And Matthew Canavan, flanked by his Nationals colleagues, said it all felt rather like the first day of school.

''It's a bit better here though because I get along much better with these teachers than I did with my actual teachers,'' he said.

The more experienced senators had plenty of advice for the newcomers.

''Take a breath, learn your surroundings and don't make rash statements,'' said Senator Madigan.

Labor's Doug Cameron advised them not to panic when they didn't understand what was going on, while iSenator Xenophon urged them not to be forced into gagging debate on the carbon tax repeal.

Labor senator Sam Dastyari had similar wisdom to share: ''Don't let them bully you, don't work on their timetable.''

Senator Day said his fellow debutants were eager to prove their critics wrong.

The Family First senator noted the crossbench had been called ''a mish-mash, flotsam and jetsam, bunch of barnyard (animals), licorice all-sorts, Star Wars aliens''.

''All those things we think are hilarious,'' he deadpanned. ''We're all committed to doing a good job.''

with Matthew Knott and AAP

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