The Russian president is due to arrive in Brisbane for the G20 summit at a time of heightened tension with host Australia, which has sent three ships to its northern coast after a flotilla of Russian navy ships appeared there this week.
Abbott said the appearance of the four Russian vessels, which include a heavily armed cruiser and destroyer, were "part of a regrettable pattern" of growing Russian military bullishness.
Cameron, speaking to the Australian parliament, warned Russia it faced further sanctions if it did not commit to resolving the conflict in Ukraine, calling Moscow's actions "unacceptable".
"It is a large state bullying a smaller state in Europe. We've seen the consequences of that in the past and we should learn the lessons of history and make sure we don't let it happen again," he said.
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Kiev and the West claim the plane was blown out of the sky with a missile supplied by Russia, an allegation Moscow denies.
The British leader described Russia's activities as a "large state bullying a smaller state in Europe," while Abbott told Putin to "come clean and atone" for the shooting down of Flight MH17.
"Russian action in Ukraine is unacceptable," Cameron told reporters before heading to the summit of the world's richest nations.
The European Union, the United States and Australia are among countries that have imposed sanctions on Russia for what they see as Moscow's desire to redraw modern Europe's borders.