Fifa has postponed the bidding process for the 2026 World Cup in light of the ongoing investigations into the award of the 2018 and 2022 tournaments.

Its secretary general Jérôme Valcke, under pressure over a $10m payment from South African World Cup organisers to the former Fifa vice-president Jack Warner that US prosecutors say was a bribe, confirmed the move at a press conference in Russia, saying it would be “nonsense” to begin the process in the current climate.

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Amid the crisis caused by US charges against 14 football officials, and guilty pleas from four more, Fifa decided that bidders from any confederation except Asia could bid for the 2026 tournament and that a decision would be made by the 209 member associations in May 2017.

However, Valcke said the process had now been postponed. The US, Mexico and Canada were expected to be among the bidders.

Swiss prosecutors and the FBI are both looking into the controversial bidding process for the 2018 tournament, to be played in Russia, and the 2022 World Cup, awarded to Qatar. A disputed summary of a Fifa ethics committee report last year ruled there was not sufficient evidence to strip either country of the World Cup but the head of the audit and compliance committee, Domenico Scala, has confirmed it remains a possibility if new evidence emerges.

The summary, which sparked the resignation of the report’s author Michael Garcia, detailed a list of allegations against Qatar and said Russia had been unable to cooperate because the organising committee had lost all its emails.

Following a meeting of the World Cup organising committee in Samara, Valcke insisted the Russian World Cup was on track before the qualifying draw in St Petersburg in July. “Overall the preparations for the Fifa Confederations Cup and the Fifa World Cup as well as our first major event, the preliminary draw, are well under way and on schedule,” said Valcke.

Russia’s 2018 local organising committee chairman, Vitaly Mutko, also a member of the Fifa executive committee and the country’s sports minister, said preparations were “well on track and on schedule”. He added: “There’s no doubt all the events of 2018 Fifa World Cup in Russia will go through at top level.”

The Russian president, Vladimir Putin, had been critical of the US investigation, claiming it was a plot to oust the Fifa president, Sepp Blatter, and destabilise the 2018 World Cup.

Valcke also defended Fifa’s handling of a $10m payment to a Caribbean Football Union account controlled by Warner, the former Fifa vice-president whose deputy Chuck Blazer has pleaded guilty in court of taking some of the money as a bribe to vote for South Africa to host the 2010 World Cup. The payment followed a 2008 letter from the South African Football Association to Valcke asking for the money to be deducted for the World Cup budget and sent as a legacy programme to be administered by Warner.

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“It was not Fifa’s money, it was a request from official South African authorities and SAFA,” he said. “As long as it is in line with rules we do it. I don’t understand what’s the problem and why I am such a target in this question. You [the media] have decided that after Blatter I am the head to be cut, fine, but don’t say it is because of this $10m.”

A decision on the date for the election of Blatter’s successor as president will be taken next month with 16 December one possible option. Fifa said an extraordinary meeting of its executive committee will take place in July when the date for a congress to hold the presidential election will be set.

A spokesman said: “It requires an extraordinary executive committee to confirm a date and agenda for the extraordinary elective congress. This extraordinary executive committee will convene in July, the precise date to be confirmed this week.”

Blatter confirmed his departure at a hastily-arranged press conference in Zurich last Tuesday and said he would stay as president until the election which is due to be held between December and March.