The meeting reportedly took place ahead of the two-day EU summit that began Thursday in Brussels and lasted 1.5 hours.
"For their part, the German Chancellor and French President assured the Greek Prime Minister that Greece will receive all the assistance it had requested. Merkel and Hollande pledged to maintain the status quo on the European borders until an extraordinary EU summit on March 6, when Turkey’s refugee management will be assessed," the source told reporters.
Tsipras told the German and French leaders that Greece, which "bore the greatest brunt of the migrant crisis," is the only country meeting its obligations, according to the source.
"He also said that ‘unilateral action’ will be unacceptable to Greece," the official who spoke on condition of anonymity said, adding that all three leaders agreed that Turkey and NATO’s anti-smuggling mission play a key role in resolving the crisis.
Greece has been under pressure from fellow EU member states as most of the refugees arriving in the country continue their journey through the Balkans to Austria, Germany and Sweden unrestricted. The influx of migrants has overwhelmed many European nations.
The prospect of reinstating border controls with Greece became high on the agenda last month after Austrian and Czech officials expressed their disapproval of Athens’ failure to secure its borders as migrants continue to transit through Greece.