Mr Lawrence's comments come as senior Labor figures move to end speculation Mr Rudd's time as leader is nearing an end, as he and the party take a dip in the opinion polls.
Western Australian Labor senator Mark Bishop said the government's proposed mining tax "is causing immense problems for the re-election of the government".
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"It needs to be addressed urgently and resolved. Only then will the government be able to punch through," he said.
But Mr Lawrence said unions backed Mr Rudd to win the federal election and would not support a switch to deputy Julia Gillard, but he warned that victory "does require everybody knuckling down to that task".
"I'd appeal for unity, for all parts of the Labor movement to get behind the leadership collectively," he said.
Treasurer Wayne Swan on Monday declared "the party is 100 per cent behind Kevin Rudd".
