Almost three quarters (71%) of Tory voters think that Immigration to the UK has increased the threat of terrorism.
Polling from Survation also found that Conservative supporters believe immigration has weakened Christian values (60%) and led to an abandonment of the white-working class (68%).
The research, commissioned by thinktank Bright Blue, revealed that only a minority of Conservatives believe immigration has increased understanding and tolerance (35%), the quality of our music and arts (39%) and the quality of sports stars (29%).
But Conservatives believe most strongly that immigration has led to communities living separate lives (85%).
Bright Blue, in light of the research, called on the Conservative Party to talk about the positives as well as highlighting the challenges immigration brings.
"This balance is needed to enable the Conservative Party to speak to defectors and the joiners and considerers it needs to command a majority at the General Election," said Ryan Shorthouse, the director of Bright Blue.
"In his recent speech on immigration in late November 2014, the Prime Minister began by talking about the benefits of immigration, listing the contribution different immigrant communities have made to Britain and concluding that 'we are Great Britain because of immigration, not in spite of it'.
"He then went on to talk about the pressures immigration brings, on our welfare system, social housing and public services. This balanced messaging is critical for the Conservative Party to sustain a broad coalition of voters within the Conservative universe."
The report also found that the most important policy relating to immigration for Conservatives is restricting migrants' access to benefits.
"This is more significant than tightening the immigration cap on non-EU migrants or withdrawing from the EU principle of free movement of workers, which are more important to UKIP supporters," Shorthouse added.
The findings come after the Office for National Statistics (ONS) revealed that net migration to the UK surged to 243,000 in the year ending March 2014.
The figures indicate that it is unlikely that Cameron will fulfil his promise to reduce net migration to less than 100,000 by May 2015.
The Tories face increasing pressure on immigration from Ukip, who want to withdraw from the EU and stop mass immigration the UK.
The latest opinion poll from YouGov for The Sun put the Conservatives on a two-point-lead over Labour (32% vs 30%) but the research also puts Nigel Farage's party on 15%.