The phrase "a careful response" is correct and usable in written English.
You can use it when referring to a reply that is thoughtful, deliberate, and considers the implications of the situation.
Example: "In light of the sensitive nature of the issue, I believe we should provide a careful response to the inquiry."
Alternatives: "a thoughtful reply" or "a measured answer."
Both cases would require a careful response from the Obama administration.
A Careful Response As video images and eyewitness accounts of the assault began to spread through social media, President Obama was easing back into his routine after a week away on Martha's Vineyard.
These questions are important and deserve a careful response.
Under demanding circumstances - and despite continued criticism - the Ecumenical Patriarchate and His All-Holiness Ecumenical Patriarch Bartholomew calibrated a careful response.
Mrs Clinton went out of her way to stress the army was well respected, was now instrumental in keeping order without attacking protesters and had a delicate line to walk - and Washington was "encouraging a very careful response".
"Does that put you in an impossible position?" A look of exasperation passed across Ivanka's face before she composed a smooth, careful response.
Howard was asked directly about his future and gave a predictably careful response, saying, "That has nothing to do with right now".
A professional, caring, and careful response can help mitigate the damage and comfort the families of victims.
Margaret Tracey, Wendy Whelan and Mr. Neal were as impressive, but there was little for them to do in this literal, careful response to a score attributed to the 18th-century composer Unico Wilhelm Graf van Wassenaer.
"No," said Alessandro Del Piero in careful response to an inquiry last week.
Putting the substance of the charges aside, Mr. Cain's most egregious campaign mistake over the last 48 hours has been his apparent refusal — or inability — to craft a careful, consistent response, despite the 10 days advance notice Politico gave him.
