The phrase "accepting a petition" is correct and usable in written English.
It can be used in contexts where an individual or organization is agreeing to consider or act upon a formal request or appeal.
Example: "The city council is currently in the process of accepting a petition for the new park development."
Alternatives: "acknowledging a petition" or "endorsing a petition".
Last year, the State Fish and Wildlife Conservation Commission, whose members the governor appoints, accepted a petition from boating groups seeking a new study of whether manatees should remain protected under state law.
Celia W. Dugger (NYT UNITEDD NATIONS DEATH PENALTY PETITION -- Secretary General Kofi Annan accepted a petition signed by over three million people from 130 countries calling for a worldwide moratorium on the death penalty.
In response, the Obama administration recently accepted a petition, filed by the United Steelworkers under Section 301 of the 1974 Trade Act, to investigate China's state support for clean-energy exports.
In a blow to farmers along the Oregon-California border, Interior Secretary Gale A. Norton refused to accept a petition today that sought reversal of a decision that has shut off irrigation water to about 200,000 acres of farmland.
A special election on whether to incorporate as a village could be held in the hamlet of Sagaponack as soon as next month, now that the Town of Southampton has accepted a petition signed by 538 eligible voters.
In a 68-page court document, Judge Garzón accepted a petition to investigate the forced disappearances of thousands of people who, like García Lorca, were on or linked to the losing Republican side of the Spanish Civil War.
The police said they arrested the women in response to a request by Mr. Macklowe's security staff, which had refused to accept a petition that the women wanted to give to the mission, and locked the doors to the building instead.
On Sept. 25, 2007, the general counsel of the court called her at home in the late afternoon to tell her that lawyers for the condemned man, Michael Richards, had asked if she would keep the court open past 5 p.m. to accept a petition.
The transfer was ordered by Spain's Culture Minister, Íñigo Méndez de Vigo, who used special temporary powers to accept a petition by a judge in Aragon.
