Mr Jones visited the European Commission in Brussels to ask for funding for upgrades to public transport as part of the £600m scheme.
He wants assurances the request will not be affected by Brexit negotiations.
The UK government has said any successful application for EU funding would be guaranteed by Westminster after Britain leaves the union.
The Metro scheme promises better trains, faster buses and light rail or tram services in Cardiff and the south Wales valleys.
Plans include £125m from UK government funds and £369m from the Welsh budget as well as EU funds, but the latter has not yet been applied for.
Welsh ministers are working towards making an application for funds by mid-2017, with construction to begin in 2019 and completion by the end of 2022.
Mr Jones, who visited Brussels on Wednesday for the fist time since the Brexit vote, said: "The EU referendum result has undoubtedly raised concerns about the delivery of our major capital programmes which currently receive funding from Europe."
He said he was in Brussels "to personally seek assurance from the European Commission that we can rely on their continued support for the Metro project in the months and years ahead.
"It is vital we keep up the momentum so we can secure approval before the UK leaves the EU."
Head of the European Commission Office in Wales, David Hughes, said: "As long as the UK remains a member state of the EU, it has the same rights and obligations as other member states.
"This means funding applications will be treated in the same way.
"With regard to what happens after the UK leaves, we simply cannot comment at this stage, since the UK has neither given notification under Article 50 of its intention to leave nor any indication of what it is seeking, either in terms of the future relationship it seeks or any transitional arrangements."
First Minister Carwyn Jones has asked for £110m in EU funding for the South Wales Metro project.