The phrase "asserted they would" is correct and usable in written English.
It can be used when reporting someone's claims or statements about their intentions or future actions.
Example: "The committee asserted they would complete the project by the end of the month."
Alternatives: "claimed they would" or "stated they would".
Should this happen -- and Democratic leaders asserted they would do everything they could to make sure it would not -- it could dilute the anti-Pataki vote.
Even if the strikes are somewhat limited, the official asserted, they would discourage the Assad government from again using chemical weapons and that, in any case, the condition of Syrian forces would weaken over time.
Alan Watkinson, a former PE teacher of Olympic 10,000m champion Mo Farah, said he was very concerned at the state of national school sport, but added that he was delighted that Miliband and Cameron had asserted they would work cross party for the future.
For someone to have killed Rebecca, as Ms. Bremner and the cable news talking heads have repeatedly asserted, they would have had to have been wearing a space suit and somehow levitated over the scene.
Hindu chauvinist organizations close to the ruling party asserted they would seek to convert Muslims back to Hinduism, arguing that even those whose ancestors had converted centuries ago should return to the fold of their ancient faith.
On Monday, Trump also released a video (see below) in which he singled out two people who asserted they'd been scammed by his seminar company.
Omar and Waj bond by asserting they would happily kill the other if necessary.
Had Atari known the "true financial condition" of Federated, company officials assert they would never have offered as much as they did for the retail chain.
And while the court of public opinion can deem Valle irretrievably monstrous, the legal system should more readily withhold judgment of guilt to the angry, the impressionable, the wrongheaded and even the vile who are caught in the cross hairs of a judicial rationale that asserts "they would have done it" and throws away the key.
By 2 p.m., firefighters said they didn't know whether flames had charred any homes in the area, asserting they'd inspect neighborhoods once the blaze had cleared.
The indictment charges the dad-and-lads team with making false statements about the company's off-balance-sheet debt and inflated operating results, and asserts they'd used the company as the "Rigas family's personal piggy bank," vis-à-vis the improper use of company funds for everything from personal loans to the construction of a $13 million golf course on the patriarch's property.
