Anwar's legal team argues that the assembly law is unconstitutional because it violates guarantees of freedom of assembly.
Anwar and two opposition party colleagues were charged last week with breaking a controversial new law outlawing street marches and violating a court order specifically banning the rally from the centre of the capital Kuala Lumpur.
Tens of thousands gathered on April 28 to demand reform of an electoral system that critics say is biased toward the coalition that has ruled Malaysia since independence in 1957.
Some protesters breached a security barricade and were met with tear gas and water cannon, touching off clashes with police that saw more than 500 people arrested.
Anwar has dismissed the charges as a ploy to remove him from politics ahead of elections that must be called by early next year.
His legal team filed applications Monday at the Kuala Lumpur court to strike out the charges, lawyer Ram Karpal said.
They argue that the assembly law is unconstitutional because it violates guarantees of freedom of assembly, while the court order banning protesters from a central square did not specifically name Anwar, he said.
Anwar, who has pleaded not guilty and vowed to fight the charges, could be fined up to RM10,000 for the charge under the assembly law.
Anyone fined more than RM2,000 for a crime is barred from contesting elections for five years although they can run while any guilty verdict is on appeal.
In January, Anwar, 64, was acquitted of sodomy in a long-running trial that he claimed was engineered by the government of Prime Minister Najib Razak after the opposition coalition made unprecedented inroads during elections in 2008.
Anwar, a former deputy prime minister, was previously imprisoned for corruption and sodomy after he fell out with his then boss, former premier Dr Mahathir Mohamad, in 1998. He was released from jail in 2004 after the sodomy conviction was overturned.