Maas said he was favourable “to proposals on strengthening Frontex” recently put forward by the European Commission, the EU's executive arm.
He held a meeting with Greek counterpart Nikos Kotzias in Athens as EU leaders in Salzburg agreed to open talks with Egypt and other North African countries on limiting migration flows.
The German minister argued that even EU member states currently refusing to accept migrants could have an “active participation” in the upgraded force.
Countries taking a hard stance on migration – such as Hungary, Poland and the Czech Republic – can make a financial contribution or help patrol borders, he said.
“I hope such an agreement can be found soon… We need a solution in the Mediterranean,” Maas said.
Greece has been overwhelmed by a recent spike in arrivals from Turkey, combined with its own slow asylum procedures and the refusal of other European states to accept more refugees.
Though an EU-Turkey agreement in 2016 drastically limited the flow, Greece has so far recorded more than 21,700 arrivals by sea this year compared to 17,500 for the whole of last year, the Greek migration ministry said this week.
“We need to think on how we can better apply the EU-Turkey agreement,” Maas earlier told Greek daily Kathimerini.
Conditions are worse on the island of Lesbos and specifically in the camp of Moria, which is housing nearly 9,000 people, about triple the nominal capacity.
In addition to frequent outbreaks of violence, rights groups say the camp sewage system has broken down, with toilet water reaching tents and mattresses where children sleep.
Medical charity Doctors Without Borders (MSF) this week said its teams have witnessed multiple cases of teenagers attempting to commit suicide.
Greek Finance Minister Euclid Tsakalotos this week said he was “of course” shocked by images of the camp, but added: “I'm shocked even more by the indifference of other Europeans on this issue.”
Greece has pledged to remove some 2,000 people from Lesbos by the end of the month, while work to improve the sewage system at Moria will begin “immediately”, Migration Minister Dimitris Vitsas said Thursday.