Christine Lagarde Yanis Varoufakis
Greek Finance Minister Yanis Varoufakis talks to International Monetary Fund managing director Christine LagardeReuters

The pressure on Greece to repay its debt to the International Monetary Fund on 5 June is increasing after the country missed its self-imposed deadline on 31 May.

A phone call between German Chancellor Angela Merkel, French President Francois Hollande and Greece's PM Alexis Tsipras on 31 May, which discussed the repayment was "constructive", said the German government, Reuters reported.

Greece has to repay a quarter of its £1.5bn ($2.28bn, €2.08bn) June repayment on 5 June. On 30 June its bailout programme expires.

Andrew Lilico, executive director of Europe Economics said that a deal with the IMF is unlikely for Greece and that unless the government collapses and a big gesture is made in Greece, the country will probably have to leave the Euro by the end of the year.

"It has been unlikely for years that they were going to make it," Lilico told IBTimes. "They should have taken action back then. If they make it out alive this year they will be fine. If you survive these shenanigans, you can survive anything."

Lilico said that no one will lend money to Greece without a third bailout.

Greece's government was on the edge of a split when MPs from ruling party Syriza signed a letter to Tsipras saying they disapprove of economist Elana Paniritis as Greece's IMF representative.

Paniritis has shown support for Greece's bailout programme, which makes her unacceptable candidate according to MPs of radical left Syriza.

"As I never sought this post, and given that I accepted it exclusively to help the government based on my experience on the way the IMF works (and other corresponding organisations) it is impossible for me to accept my appointment in the midst of the negative reactions of Syriza's MPs and cadres," Paniritis said in a statement.

Paniritis's withdrawal is only one of the aspects increasing tension in Greece, as Kristine Lagarde, head of IMF said that a Greek exit (Grexit) from the eurozone is a possibility.

"We have rules, we have principles. It cannot become a half-baked program revision," Kristine Lagarde told German newspaper Frankfurt Allgemeine Zeitung.