The Taoiseach has confirmed that he has sought a meeting with the Fianna Fáil leader Micheál Martin to begin negotiations to renew the confidence and supply deal which expires after the next budget.
Mr Varadkar said he had met the Fianna Fáil leader today in relation to Dáil reform.
Mr Martin has consistently said he will not begin negotiations until after the budget.
However, the Taosieach wants the talks to begin before October.
He has citied Government stability and Brexit as reasons to bring forward the negotiations.
Responding to questions from Labour party leader Brendan Howlin in the Dáil earlier, Mr Varadkar said: "It's my preference that we would have already started discussions on the renewal [before October].
"I don't think it is in the country's interest for us to be trying to negotiate an extension to the Confidence and Supply agreement in October and November when we are dealing with the Brexit negotiations and so many other different matters."
He added: "That's a matter I will discuss with the leader of the Opposition in due course."
The Labour leader said that "the instability of the British government makes your Government look very stable.
"However, there has been much speculation about the prospect of a September election. The Confidence and Supply is scheduled to be reviewed at the end of this year and the third budget to be passed."
He asked the Taoiseach to confirm that he will introduce a Budget in September, questioning if it is his intention to introduce a Social Welfare Bill and a Finance Bill in the autumn.
He also asked when the Taoiseach's preference date is to open discussions with Fianna Fáil on the renewal of the Confidence and Supply agreement.
The Taoiseach said it is "absolutely the intention that the Government will introduce a budget in October."
Fianna Fáil has said no date has yet been agreed for the party leader and the Taoiseach to meet in relation to the Confidence and Supply deal.
Micheál Martin confirmed earlier this week that contact had been made between the two sides.
He reiterated that the negotiations to renew the deal should not begin until after the Budget.
Meanwhile, regulation and clinical guidelines to make abortion services available to Irish women from January are currently being worked on according to the Taoiseach.
In the Dáil, Mr Varadkar reiterated the Government's intention to have the abortion legislation brought before the Dáil in September.
Responding to Catherine Murphy of the Social Democrats and Solidarity/People Before Profit TD Ruth Coppinger, he said the legislation would be open to amendments by TDs in the Dáil.
Also in the Dáil, Mr Varadkar said that it is still the Government's intention to establish the Commission of Inquiry into the CervicalCheck controversy in September.
During Leaders' Questions, Sinn Féin leader Mary Lou McDonald asked if the Dáil could be recalled during the summer to ensure the prompt establishment of the inquiry after Dr Gabriel Scally completes his report into the issue.
She said the Government has no sense of urgency or seriousness in addressing the CervicalCheck issue.
She accused the Government of not putting the victims and their families first and said "delay and obstruction have been the overriding themes of the Government's handling of the scandal."
Ms McDonald said the scoping exercise was supposed to offer a short inquiry as some of the women are so ill.
She said the Government has not really prioritised the matter or has not got a sense of the urgency of the matter.
Ms McDonald claimed women are being sent into an information cul-de-sac by the HSE and the Department of Health when they try to claim their €2,000 payment.
She said no account is being taken of the considerable expenses they have incurred. She asked when the review of the 3,000 smear tests will commence, when will Dr Scally report and will the Dáil be recalled on the publication of the report to set up the inquiry.
The Taoiseach said this is an issue that Government has given a lot of focus to.
He acknowledged it has been a difficult issue to deal with as the Government did not have all the facts.
He said a serious incident managmenn team has been set up and sent in to CervialCheck to ensure women get information as quickly as possible.
He said the scoping inquiry is under way and the Government will receive interim reports from Dr Scally.
He said that there is an agreement with the IMO to give women repeat smears if they request them.
He acknowledged the Government expected the review would be completed more quickly but it will take three or four months.
He asked for details of the individuals that are having difficulty accessing the payment and he said retrospective expenses are not available and repeated that mediation is available to those affected.
Ms McDonald asked again about when the review of 3,000 cases will commence.
The Taoiseach said he cannot say for certain when the examination of the slides will take place but he anticipates that will commence soon.
He said it is intended that the Commission of Investigation will begin in September, subject to the approval of the Dáil.
Additional reporting Conor McMorrow