Deputy Prime Minister Barnaby Joyce has admitted the Coalition was wrong to deny a Labor MP time away from Parliament to care for a sick child, as tensions flared over Labor's plans to make it difficult for government MPs to miss critical votes.

Revenue and Financial Services Minister Kelly O'Dwyer said Australians wanted Parliament to focus on the national interest and not play political games, challenging Labor leader Bill Shorten to match his promises to be constructive with actions.

Labor said on Tuesday it would test the Coalition claims that it has a "working" majority in the new Parliament by not entering into a formal pairing arrangement, which could effectively deny government MPs holidays or sick leave.

Shadow treasurer Chris Bowen indicated a slightly less aggressive approach to pairing on Wednesday, saying that Labor would allow Coalition MPs a pair in situations in cases of "national interest" and where there were "compelling personal reasons".