Foreign Affairs Minister Charlie Flanagan has said he understands that a decision over Fine Gael leadership will be made 'soon'.
Enda Kenny has again come under pressure to outline his plans for stepping down as party leader and Taoiseach.
Mr Kenny previously indicated he would deal with his departure after last month's Brexit summit.
Leo Vardakar and Simon Coveney are seen as the frontrunners in any leadership contest, with a number of other senior ministers yet to reveal whether they will put their names forward.
Speaking on Newstalk yesterday, Fianna Fáil leader Michéal Martin said that the Taoiseach "needs to set a date" for his departure.
He argued: "It's been dragging out for far too long. There has been a degree of inertia.
Speaking about the impact the Fine Gael leadership contest is having on Government, he argued: "You can't be running for a leadership election [...] and at the same time manage a department. I think decisions are being postponed because of the vacuum."
On Newstalk Breakfast this morning, Minister Flanagan said: "There is continuing speculation about the future of my party leader and Taoiseach Enda Kenny. I understand that a decision will be made on this issue soon.
"I expect there will be announcements and development in this matter over the next few weeks."
Minister Flanagan also spoke about the ongoing issues surrounding Brexit.
Referencing the suggestions of worsening relations between EU and British leaders ahead of the start of formal Brexit negotiations, he observed: "There's a lot of hype involved... a lot of rather amusing comment and hyped up comment regarding the famous dinner of last week.
"We've got to remember we're in election mode in Britain - oftentimes things are said in the course of an election campaign, in terms of rhetoric, that mightn't necessarily be reflective of the true position.
"I would say to all the parties - to the UK and indeed the EU negotiators - we need to come here with an element of goodwill."
The EU's chief Brexit negotiator Michel Bariner is visiting Ireland this week, and Charlie Flanagan intends to take him to the border with Northern Ireland to meet with some of the farmers, business people and students who travel across it daily.
"I'm looking forward again to impressing upon him the need to ensure [...] that our border with Northern Ireland remains open," Minister Flanagan said.
