The position of Fifa’s powerful secretary general, Jérôme Valcke, is likely to come under intense pressure after new evidence emerged that showed he was aware of a $10m payment from South African officials to Jack Warner described by US investigators as a bribe.

The revelation will also put the embattled Fifa president, Sepp Blatter, recently re-elected for a fifth term, under renewed pressure over whether he knew about the 2008 payment and what it was for.

Just an hour after Fifa had released a statement denying that Valcke authorised the transfer of $10m to a Bank of America account linked to Warner, a letter from the South African Football Association was obtained by the Press Association that was addressed to the longstanding Fifa secretary general. It showed he was aware of it and contained detailed instructions for payment.

Fifa’s statement had said neither Valcke, Blatter’s longtime closest ally and fixer, nor the president himself “were involved in the initiation, approval and implementation of the above project”.

The payment is at the heart of the Fifa bribery scandal - a US department of justice indictment of 18 people, including 13 Fifa executives, on corruption charges says the money was paid to Warner and his deputy, Chuck Blazer, in return for them voting for the 2010 World Cup to be played in South Africa.

The indictment states that “a high-ranking Fifa official caused payments … totalling $10m – to be wired from a Fifa account in Switzerland to a Bank of America correspondent account in New York … controlled by Jack Warner”.

The letter, seen by the Guardian, was dated 4 March 2008 and contained detailed instructions on how the money should be paid. The SAFA president, Molefi Oliphant, asks for the $10m to be deducted from the $423m due to the organisers of the World Cup by Fifa and instead routed to a “diaspora legacy programme” controlled by Jack Warner, the disgraced former president of Concacaf.

BOMBSHELL: Letter from South Africa FA to FIFA instructing $10m payment to Warner WAS addressed to Jerome Valcke pic.twitter.com/b0yKBPRAcA — Martyn Ziegler (@martynziegler) June 2, 2015

The letter from Oliphant to Valcke reads: “In view of the decision by the South African government that an amount of USD 10million from the organising committee’s future operational budget funding and thereafter advances the amount to the Diaspora Legacy Programme. In addition, SAFA requests that the Diaspora Legacy Programme be administered and implemented directly by the President of Concacaf who shall act as a fiduciary of the Fund.”

A Fifa response read: “The letter is consistent to our statement where we underlined that the Fifa Finance Committee made the final approval.”

According to the US indictment, the money was siphoned off into Warner’s personal accounts and he paid $750,000 of a promised $1m to Blazer.

Warner, among those charged in the US, said after his arrest last week: “If I have been thieving money for 30 years, who gave me the money? How come he is not charged?”

American prosecutors last week accused nine senior current or former Fifa officials – seven of whom, including the Fifa vice-presidents Jeffrey Webb and Eugenio Figueredo, were arrested in dawn raids at a five-star hotel in Switzerland – of “hijacking” international football to run “a World Cup of fraud” to line their pockets by $150m.

In the indictment that followed the arrests last Wednesday, it was alleged that the $10m payment from South Africa was routed to the Caribbean in return for World Cup votes.

Fifa’s statement, released this morning in the wake of overnight reports in the New York Times that Valcke was the unnamed senior official named in the indictment, said the French secretary general was not involved.

It said the payment was made at the request of the South African government and FA, and authorised by the Argentinian Julio Grondona, the former chairman of Fifa’s finance committee and long-time ally of president Sepp Blatter. Grondona died last year.

Fifa insisted Valcke nor any other senior management figure was involved. At a press conference on Saturday Blatter was asked about his knowledge of the $10m payment and replied: “Definitely that’s not me. I have no $10m.”

The Fifa statement said: “The payments totalling USD 10m were authorised by the then chairman of the Finance Committee and executed in accordance with the organisation regulations of Fifa. Fifa did not incur any costs as a result of South Africa’s request because the funds belonged to the LOC. Both the LOC and SAFA adhered to the necessary formalities for the budgetary amendment.

“Neither the Secretary General Jerome Valcke nor any other member of Fifa’s senior management were involved in the initiation, approval and implementation of the above project.”

It also said: “SAFA instructed Fifa that the Diaspora Legacy Programme should be administered and implemented directly by the President of Concacaf who at that time was Deputy Chairman of the Finance Committee and who should act as the fiduciary of the Diaspora Legacy Programme Fund of USD 10m.”

The reference to Warner, who as deputy chairman of the finance committee was involved in discussions over effectively approving a $10m payment to himself, itself raises questions about Fifa’s processes.

In Paraguay on Monday a judge ordered house arrest for the former president of South America’s soccer federation Nicolás Leoz, accused of involvement in the scandal. And in Brazil, a new inquiry has been launched into the controversial dealings of Ricardo Teixeira, the former head of the Brazilian football association, who is accused of making $150m in kickbacks. One of his successors, José Maria Marin, was among those arrested last week.

Following Blatter’s re-election as Fifa president the English Football Association’s chairman, Greg Dyke, said his organisation would support any boycott led by Uefa, who will meet on Saturday in Berlin ahead of the Champions League final.

The English Football Association board member Heather Rabbatts announced she was withdrawing from Fifa’s task force against racism and discrimination with immediate effect. “Like many in the game I find it unacceptable that so little has been done to reform Fifa,” she said.