"We are unsatisfied with the court ruling and we have appealed," Deputy Attorney General Fred Ruhinda told AFP, adding that the appeal has been lodged at the Supreme Court, the country's highest court.
"The law was not intended to victimise gay people, it was for the common good."
Branded draconian and "abominable" by rights groups but popular domestically, the six-month old law which ruled that homosexuals would be jailed for life was scrapped on a technicality by the constitutional court on August 1.
Judges ruled it had been passed in December without the necessary quorum of lawmakers in parliament.
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US Secretary of State John Kerry had likened the law to anti-Semitic legislation in Nazi Germany, and Western nations made a raft of aid cuts to Uganda's government.
Today, activists gathered for their first gay-pride march since the law was overturned, waving rainbow coloured flags in celebration.
Critics said President Yoweri Museveni signed the law to win domestic support ahead of a presidential election scheduled for 2016, which will be his 30th year in power.
Analysts suggest the surprise court hearing last week was encouraged by Museveni, so as to quash the law without appearing to cave in to foreign pressure.
But lawmakers this week also signed a petition calling for a new vote on the bill, and to bypass parliamentary rules that require it be formally reintroduced from scratch -- a potentially lengthy process, with the last such bill taking four years from introduction to the final vote.
"Our prayer is that the Speaker waives house rules of procedure, to enable us to pass the bill without going through the three stages of the reading," said lawmaker Latif Sebagala, a member of the opposition Democratic Party.