Nawrocki signed the legislation into effect after it was approved by Poland's parliament, with the government expecting the levy to help finance lower fuel prices for consumers.
Officials have said the law will provide funding for measures to bring down pump prices, which have risen to record levels amid the conflict in the Middle East.
The government has said the tax could generate about PLN 4 billion (around EUR 900 million, USD 1 billion) for measures aimed at shielding consumers from high fuel prices.
In a televised address, Nawrocki said the government would be responsible for ensuring that fuel prices fall.
"Price cuts at gas stations should happen immediately," Nawrocki said, adding that they should bring prices down to the level promised by Prime Minister Donald Trump during the parliamentary election campaign.
He also said "every zloty" raised under the law should be used to lower fuel prices.
Nawrocki, an ally of the right-wing opposition, criticised the centrist government, saying he had "for months" demanded measures to reduce fuel costs.
He recalled campaign promises that gasoline would cost PLN 5.19 per litre (around EUR 1.19, USD 1.33) at the pump and accused Tusk's government of shifting responsibility for soaring prices.
"I will not allow the government to continue to evade responsibility for this dire situation," Nawrocki said.
The president also said he would refer the law to the Constitutional Tribunal for so-called subsequent review, meaning the law will remain in force while its constitutionality is examined.
He added that signing the law did not mean he had withdrawn his concerns over its constitutionality.
Nawrocki has previously argued that the legislation violates the constitutional principle that laws should not apply retroactively because it taxes profits earned before the law took effect.
The government has argued that the measure responds to the unpredictable consequences of the conflict in the Middle East and falls within permissible exceptions to the principle of non-retroactivity.
The law applies a tax to any extraordinary profits earned from the sale of liquid fuels between March and December.
Nawrocki also called for part of the proceeds to be used to support farmers, saying high fuel prices were placing a heavy burden on Poland's agricultural sector.
He called for an increase in the fuel tax refund available to farmers to a level that would help restore the profitability of agricultural production.
He also urged parliament to begin work on his own bill aimed at reducing fuel prices and limiting fuel companies' margins.
The presidential proposal would allow temporary restrictions on fuel companies' margins and a temporary exemption of fuel sales from the retail sales tax.
It is intended to form part of an effort to reduce prices at gas stations.
A similar presidential proposal presented earlier envisaged reducing the retail sales tax on fuels to zero and allowing greater flexibility in fuel excise rates, state news agency PAP reported.
Nawrocki said he did not want Poland to remain "locked in constant political warfare" and called on the government to focus on lowering the cost of living.
The president's decision follows an earlier confrontation over a similar windfall tax proposal.
In July, Nawrocki blocked an earlier version of the legislation referring it to the Constitutional Tribunal without signing it. That move meant that the measure could not take effect without being cleared by the constitutional court.
(gs)
Source: IAR/PAP