A meeting of the culture, science, education and media committee in Paris on Tuesday on "Good governance and ethics in sport" passed a draft resolution calling on FIFA to launch an inquiry and to speed up their reforms.
Blatter was re-elected in June last year after rival candidate Mohamed Bin Hammam withdrew after he was charged with bribery - and in July was banned for life.
Football Association chairman David Bernstein appealed unsuccessfully for the election to be postponed, and the committee of the Council of Europe - the watchdog body which oversees the European Court of Human Rights - believes the election process should now be scrutinised.
The draft resolution states: "The Assembly specifically calls on FIFA to take the necessary steps to cast full light on the facts underlying the various scandals which, in recent years, have tarnished its image and that of international football.
"The Assembly insists that FIFA... open an internal investigation in order to determine whether, and to what extent, during the latest campaign for the office of president, the candidates, and particularly the successful candidate, exploited their institutional positions to obtain unfair advantages for themselves or for potential voters."
Bin Hammam was banned after being found guilty of offering cash gifts of 40,000 US dollars each to 25 officials from the Caribbean at a meeting three weeks before the FIFA election.
Blatter's campaign tactics were also questioned when he announced to the CONCACAF federation extra funding of one million US dollars.
The resolution also calls on FIFA to publish in full all documents it has in relation to the ISL court case, in which four current or former FIFA members are understood to be named as having taken kickbacks from the organisation's marketing firm during the 1990s.
The report to the committee by Francois Rochebloine, from France, says presidential terms of offices for all sporting organisations should be limited.
It points out that as well as football, the international federations of athletics, tennis, gymnastics, handball and skiing - among others - all have presidents who were elected during the 1990s.
Meanwhile, Blatter has asked for talks with Brazil's president Dilma Rousseff next week as concerns grow about the collapse in the relationship between the organisation and the 2014 World Cup hosts.
The troubled partnership hit an all-time low at the weekend following criticism of delays by FIFA secretary general Jerome Valcke, with the Brazilian government responding by saying they no longer wanted to deal with him.
A written apology from Valcke came on Tuesday, followed up by Blatter to Brazil's sports minister Aldo Rebelo. But Blatter's letter also makes clear that time is running out.
Blatter's letter states: "Please allow me to express my deepest regret for the present situation. I am gravely concerned about the deterioration in the relationship between FIFA and the Brazilian government, a relationship that has always been characterised by mutual respect.
"You have also received a letter from the FIFA secretary general Jerome Valcke and I have no further comment on this matter other than to say that both as FIFA president and personally, I would like to apologise to all those - above all the Brazilian government and President Dilma Rousseff - who feel that their honour and pride has been injured."
The letter adds: "Brazil deserves to host the World Cup and the entire world is looking forward to it. However, the sands of time have been running since 2007.
"Therefore, let us not waste time on entrenching our positions. Let us instead build something great together. I would like to meet President Rousseff and yourself as soon as possible - ideally next week."
According to the Council of Europe committee report, in 2010, the total wage bill at FIFA was 65.3million US dollars, making average annual pay per staff member as 168,700 US dollars.
"FIFA's spending on salaries rose by 31.6% between 2009 and 2010, while the average number of staff members increased by only 7.2% over the same period," says the report.
"The financial report does not explain these increases and gives no information about the salaries of key management personnel."
FIFA pointed out their ethics committee had already investigated Blatter over his campaign and said the reform process was well under way.
A FIFA statement said: "Regarding the ethics proceedings on President Blatter, all charges were dismissed in full, as the ethics committee found that no breach of the code of ethics had been committed."
FIFA added that the 31% rise in salaries was mainly due to the strengthening of the Swiss franc against the US dollar - the organisation is based in Switzerland but for accounting reasons salaries are converted to dollars.
FIFA added they intended to publish the ISL report as soon as they were given permission by the Swiss courts.