In a letter to the PM, the group of 27 charities - including Oxfam and Amnesty International - say the UK should take a "proportionate" share of refugees.
They praise the commitment to resettle 20,000 Syrian refugees over five years but say more needs to be done.
A government spokesman said the UK has a "long and proud history of offering sanctuary" to those in genuine need.
The letter, coordinated by the British Refugee Council, asks Mr Cameron to show a "new resolve" to deal with the crisis, which saw nearly 4,000 people drown last year and hundreds of thousands more face danger and hardship while fleeing violence.
The group, which also includes the International Rescue Committee, Liberty and ActionAid, wrote: "Last year's announcement that the UK will resettle 20,000 Syrian refugees over five years was a welcome first step, 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 UK can and should be doing much more to ensure that refugees are not compelled to take life-threatening journeys or forced into smugglers' hands."
They endorse principles set out by 350 former judges and lawyers in October which include taking a fair share of refugees and establishing safe and legal routes to the UK for those seeking protection.
Refugee Council chief executive Maurice Wren 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.
"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."
The government spokesman 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 neighbouring 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."
He said the government was also providing "life-saving aid to those most in need", both in and around Syria and in Europe, and working with other countries to "ensure systems are in place which properly address unfounded claims for asylum".

The 34-year-old goalkeeper was hurt during last week's Manchester derby at Etihad Stadium, which finished 0-0.
Willy Caballero is now expected to play for the rest of the season as City look to hold on to a place in the top four and Champions League qualification.
Boss Pep Guardiola also confirmed striker Sergio Aguero will miss Saturday's game with Crystal Palace.
The Argentina international injured himself against Middlesbrough, but could return for their next Premier League match on 13 May.
"Aguero is out. Hopefully he'll be back for Leicester, but this game no," said Guardiola.
"John Stones and Bravo are out, Claudio until next season and John maybe in the next games [can return]."
Guardiola also confirmed David Silva will miss the Palace game.
David Cameron's response to the refugee crisis is "clearly inadequate", leading aid and refugee agencies claim.
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Manchester City's Claudio Bravo will miss the last four games of the Premier League season with a calf injury.