General Synod members backed a proposal by the Bishop of Durham, Rt Revd Paul Butler, which calls upon the government to work with international partners to establish safe routes for refugees.
Before a vote on the issue Justin Welby warned it meant support for military action and that the Church must put its money where it puts its mouth.
Archbishop Justin said: "I think we need to recognise though... the motion essentially commits us to supporting the use of armed forces overseas.
"The reality of working in those areas to create safe ways of routes to places of safety must include some kind of forceful response.
"It is almost impossible to see how it could be done otherwise."
Bishop Paul accepted that but stressed the backing for military action only applied to providing a safe route for refugees.
He said it was "likely that some [military action] will be needed" to provide routes to places of safety for asylum seekers.
The motion also urges diocese to work closely with local authorities to provide resources for the resettlement of refugees who arrive in the UK.
A bid by Very Revd Andrew Nunn to remove the word 'welcome' and replace it with 'acknowledge' in a paragraph which speaks about the government's promise to take 20,000 refugees between now and 2020, was rejected by Synod.
Part of the motion also suggested the government should ensure vulnerable Christians facing persecution for their faith should have this taken into account when officials decide who should be offered asylum.
Proposing the motion, Bishop Paul said: "The compassion which compels us to help the refugee will be blind to differences of creed as to colour or any other characteristic.
"For all that, it is right that we uphold the right of our fellow Christians to fair treatment.
"Whether or not they are in refugee camps, easy or hard to find, they must suffer no discrimination as UNHCR seeks out those in greatest need of resettlement.
"Those whose suffering is exacerbated by religiously motivated persecution deserve to have that factor given full weight in the calculation of need."