The stadium was the site where two workers were killed when a crane fell over last month and Blatter said there was "no plan B" if further problems were encountered.
Mid-April leaves little margin for error as the opening match is due to be held on June 12, less than two months after the revised completion date.
Blatter told a news conference in Salvador: "It will be ready in mid-April, it is a question of trust that it will be done.
"God and Allah willing no more accidents shall arise and the reconstruction can restart as soon as possible.
"For the time being there's no plan B."
FIFA also announced details of the prize money for the World Cup - a 33 per cent increase on 2010.
The winners will receive prize money of 35million US dollars (£21.5million), and even those countries that fail to get out of the group will receive 8million dollars (£5million) with every team also getting 1.5million dollars (£1m) towards preparation costs.
The amount of money given to clubs - the sum will depend on the number of players from each club - will rise to a total of 70million dollars (£43million), almost double that at the 2010 tournament.
Blatter announced that for World Cup games in hot conditions, match officials and the official FIFA doctor in the stadium will decide whether to stop games for water breaks.
The FIFA president also poured cold water on UEFA president Michel Platini's call for football to introduce sin-bins.
He said: "I cannot see why we should change something in the match control of the World Cup when we have already established all the regulations."
Blatter added that FIFA was committed to improving the conditions of workers in Qatar in the build-up to the 2022 World Cup and would draw up a plan detailing responsibilities for itself, the Qatar government, companies and labour organisations.
It follows an investigation which highlighted the shocking conditions endured by some of the one million migrant workers in the country.