Tsipras also announced that Admiral Evangelos Apostolakis, chairman of the Joint Chiefs of Staff, will replace Kammenos as defense minister.
"We worked together for four years turning around the country and pulling it out of bailouts and austerity", Kammenos told reporters. Speaking after the meeting, he said that "The Macedonia name issue. doesn't allow me not to sacrifice the minister's chair".
Greek Prime Minister Alexis Tspiras on Sunday called for an "immediate" confidence vote in parliament over the resignation of a top minister, after his coalition government collapsed in a row over a name change deal with Macedonia.
Albania has congratulated Macedonia's parliament vote on name change as "a clear demonstration of statesmanship unlocking North Atlantic Treaty Organisation and European Union path". He also said he requested Tsipras to take the Prespes deal to the Greek people in a referendum, a proposal which got nowhere.
Meanwhile, ahead of the vote in Athens, two news websites alleged that a prominent member of Greece's main opposition New Democracy party - which rejects the name deal - called on its members to phone lawmakers of the ANEL party and urge them to vote against the agreement.
Mr Kammenos said that he would vote against the government as supporting it would imply backing for the name deal with Macedonia.
In response to Kammenos' announcement, Tsipras said that he would request a vote of confidence in his government during the coming week.
Macedonian lawmakers approved the agreement late Friday. Greek parliamentary endorsement of the name is required for the tiny Balkan nation to join the European Union and North Atlantic Treaty Organisation. Polls indicate it will probably fail to obtain the minimum three percent of the popular vote needed to meet the Greek parliamentary election threshold. "But I am convinced that the Greek parliament will also find the strength to make the decision", he said. NATO Secretary-General Jens Stoltenberg and EU Enlargement Commissioner, Johannes Hahn - frequent visitors and now household names in Macedonia/FYROM - were the first to back the move, nearly in real time, with Washington's minimalist statement emerging a day later.
But a change of government in Macedonia in 2017 finally led to the deal reached a year ago. He said that he believes he can find the required six votes.
Greece has a province called Macedonia and long demanded Skopje change its country's name to remove what Athens considered to be an implied claim to Greek sovereign territory.
Zaev said he was "convinced that Greek lawmakers will recognise the historical significance of the agreement". It began almost three decades ago, with Macedonia's declaration of independence, but has roots dating back centuries.
The ancient kingdom of Macedonia - or Macedon - was a relatively small part of the present day Greek province of Macedonia.
Last June, Zaev and Tsipras reached a landmark compromise over the name dispute.