Countries opposed to military action against Syria should think about doing more to help alleviate the humanitarian crisis, International Development Secretary Justine Greening said.
With the United Nations not even half way to meeting its funding target to deal with the fallout - which has created two million refugees, it was time for states to "step up" their contributions, she said.
The decision "does not need to wait" until after any US-led strikes against the regime, she added.
David Cameron welcomed offers of new humanitarian assistance for Syria from Canada, Italy and Qatar at the G20 summit, following his announcement of an additional £52 million in British aid.
He said he wanted to "set the drumbeat" of momentum towards filling a three billion US dollar (£1.9 billion) shortfall in UN funds to assist millions of people affected by the two-and-a-half year civil war.
Ms Greening said the UK - already the second most generous donor - had "always planned" to take a leading role and was not seeking to up ints contribution as a result of the Commons vote against British involvement in military action.
In an appeal to other countries, she told BBC Radio 4;s Today: "What we can agree on surely as an international community is the need for a humanitarian response and right now that response is not great enough.
"The UN appeal is not even half funded and it's time to step up. Maybe the countries that do not favour military strikes need to ask themselves whether they can contribute more to the humanitarian effort. That does not need to wait.
"The UK yesterday, alongside other G20 countries, announced additional funding for the humanitarian crisis. I hope we will be joined in the coming days by many, many more countries."
Ms Greening, who apologised to Mr Cameron for missing the vote after not hearing the division bells, said it was right that the Prime Minister had ruled out putting the question to MPs again.