There were tensions at the Fine Gael parliamentary party meeting over the issue of pylons.
Mr Kenny told Mr Deasy that no decisions would made on the pylon issue until after the end of the consultation period.
Some 35,000 submissions have been received by Eirgrid on the proposed projects.
"Kenny told Deasy that all concerns would be taken on board. But certainly it is a very contentious issue for many of us," said one TD.
Meanwhile, Labour has appointed Social Protection Minister Joan Burton as the party's director of the local and European elections.
Mr Gilmore informed last night's meeting of the Parliamentary Party that he formally asked his deputy leader to take up the position.
The announcement has been warmly welcomed within party ranks and comes despite reported tensions between Mr Gilmore and Ms Burton in recent weeks.
It is hoped internally that the selection of Ms Burton will help steer the party away from a disastrous result at the ballot boxes.
A number of party sources said last night that they believe Ms Burton will prove effective during both the local and European campaigns.
"We know this will be a tough election but Joan served as director during the referendum on the fiscal treaty and she is definitely seen as someone who will help us in preventing a bad result," a source said.
A deputy director of elections for the party is due to be appointed in due course, with junior minister Sean Sherlock and Cork TD Michael McCarthy seen as possible candidates.