The Taoiseach has been urged to call an election this year at a private meeting of his party.
Simon Harris told a three-hour meeting of the Fine Gael parliamentary party that members must continue their work following the local and EU elections.
It is understood that Cork TD Michael Creed told Mr Harris that the Government should not wait until March to call the next general election, warning against another winter campaign.
It comes after Mayo TD Michael Ring, who was not in attendance at Wednesday's meeting, publicly called on the Taoiseach to go to the polls this year.
“I think Fine Gael would be well to go to the country. Go to the country in October, not wait. We had two winter elections and I don’t ever want to see a winter election again," Mr Ring said this week.
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With Labour TD Aodháin Ó Ríordáin already elected to Brussels, and the chance that other sitting TDs will also gain seats in Brussels, it was also suggested at the meeting that holding by-elections so close before a general election wouldn't make sense.
Mr Harris said Fine Gael will continue to concentrate on the delivery of important issues including housing, law and order, migration and disability services for children.
He added that the Government's target for homes built annually will be revisited this year to reflect the ambition required to meet demand.
Meanwhile, at a meeting of the Fianna Fáil parliamentary party, Tánaiste Micheál Martin told colleagues that he will be evaluating the performance across all constituencies and examining the vote in all areas.
He told TDs and senators that they must continue to work over the summer.
"It was very much Micheál in charge," one member said, with another senator describing the mood in the room as "positive".
"There was no sign of him, from the way he spoke, going to Europe," one source said, referring to the fact that Fianna Fáil will have to select a commissioner to put forward.
Sources said that Mr Martin singled ministers out, telling them that they must ensure that they are working for the party and delivering as much as possible in their own portfolios.
One party members said: "He was really strong and enthusiastic in stating that people do want to engage with us and that Fianna Fáil can do better. We have to work at it and we have to listen."