The group of charities, including Oxfam and Amnesty International, called on the UK to take a proportionate share of refugees.
They urged the Conservative Party leader to show a “new resolve” to deal with the crisis, during the course of which almost 4,000 refugees died in 2015.
“Last year’s announcement that the UK will resettle 20,000 Syrian refugees over five years was a welcome first step,” said the letter, which was coordinated by the British Refugee Council.
“But given the numbers of people searching for safety across the globe, this response is clearly inadequate: it is too slow, too low and too narrow.”
The charities said the UK can and should be doing “much more” to ensure refugees are not “compelled to take life-threatening journeys or forced into smugglers’ hands.”
Commenting on the crisis, the Refugee Council said there are “no easy answers” to a humanitarian crisis of this magnitude.
“However, the solution must not be to spend another year impassively watching on while desperate people drown or are forced to endure a march of misery across the continent as they try to find a safe haven or to be reunited with their loved ones,” its spokesperson told BBC News.
“This year the prime minister must open his heart and show true statesmanship by welcoming far more refugees to the UK, enabling them to travel here safely and legally to live lives free from violence, tyranny and oppression,” they added.
Insisting the UK has worked its hardest to tackle the migrant crisis, a government spokesperson said: “The United Kingdom has a long and proud history of offering sanctuary to those who genuinely need our protection, with each claim for asylum judged on its individual merits.
“The terrible images we have seen in the last year have moved us all, strengthening our resolve to help prevent more people suffering such a fate.
“That is why we are resettling people directly from the countries neighboring Syria, to which so many refugees have fled, and we have already met our target of welcoming 1,000 of the most vulnerable before Christmas.”
The UK government is providing “life-saving aid to those most in need, both in and around Syria and in Europe,” the spokesperson added, talking on customary condition of anonymity.