The phrase "acknowledging their concern" is correct and usable in written English.
You can use it when you want to express recognition or validation of someone's worries or issues.
Example: "In our response, we will be acknowledging their concern about the recent changes in policy."
Alternatives: "recognizing their concern" or "validating their concern."
But many participants, while acknowledging their concern over the increase in anti-Muslim rhetoric, said the troubles had only further encouraged them to attend this year.
Many Muslim countries, while acknowledging their concern over Iran's nuclear program, have insisted that the entire region must be made nuclear free.
In addressing the men, she dispelled their fears pre-suasively: first acknowledging their concern by admitting a weakness, which established her honesty for whatever she said next, and then following it with a strength that demolished the weakness.
Medvedev first denounced Russia's protesters before acknowledging their concerns.
By entering the lion's den, the speakers would establish what speechwriters call a "handshake" — creating a connection with detractors by acknowledging their concerns.
In July 2006, acknowledging their concerns, Norwalk's zoning department reduced the allowable heights of houses in Rowayton's densely settled neighborhoods to 30 feet from 35 feet, measuring from the ground to the midpoint of the roof's slope.
In a show of resolve, Ms. Rousseff and other authorities also lashed out at the growing violence among some of the protesters, denouncing recent attacks on government buildings, acknowledging their concerns about security ahead of a visit by the pope and, in at least one case, threatening to deploy the army to the streets if the demonstrations continued to intensify.
Lat's parents worry over his lack of interest in his studies; he acknowledges their concern but finds himself unmotivated to forgo play for academic pursuits.
Phil acknowledged their concerns and invited them to discuss modifications to the model.
For instance, a company that wants to build a controversial factory might meet with angry residents to acknowledge their concerns about possible adverse impacts.
Ms Lagarde acknowledged their concerns, but said that being European should be neither a "handicap, nor an asset" when assessing her qualifications.
