The phrase "asserting most of" is correct and usable in written English.
It can be used when you want to indicate that someone is claiming or stating a significant portion of something, often in a context of argument or discussion.
Example: "In his speech, he was asserting most of the points made in the previous debate."
Alternatives: "claiming the majority of" or "stating a large part of".
He is also seeking information on whether any other individuals and corporations were solicited in the capital campaign for which the foundation has asserted most of the money was earmarked.
To the Editor: Does the international system already have in place, as James P. Rubin asserts, "most of the rules it needs" to achieve global security and realize basic human rights?
In a video introducing GEBN, vice president Steven Blair, an exercise scientist, asserts: "Most of the focus in the popular media and in the scientific press is, 'Oh they're eating too much, eating too much, eating too much'--blaming fast food, blaming sugary drinks and so on...
The state responded to the High Court of Justice on Saturday night, arguing that the gathering would become a focus of protest that could lead to rioting, and asserting that most of the tents had been pitched on territory that Israel had declared state land.
Furthermore the defense referenced the findings of a forensic expert who didn't see any evidence of code copying in what Oculus had shipped, while also asserting that most of the "trade secrets" ZeniMax's legal team was lauding were already publicly known and that other solution to the problems already existed.
The defendants denied this, asserting that most of the participants were "illiterate peasants", while the VNQPH were dominated by members of the scholar-gentry.
Environmentalists, however, asserted that most of Mr. Pataki's objections were baseless.
The Pentagon asserts that most of those attacks have been the result of personal grudges, disputing Taliban claims to have widely infiltrated the Afghan security forces.
The government asserted that most of the money went to the village's schools, but that the men also personally pocketed some.
His lawyers also asserted that most of the information in question had been made public through reports by analysts and the media.
