WASHINGTON (CNN) -- Former Sen. John Edwards fired back Tuesday at an adviser of likely presidential rival Sen. Hillary Clinton who claimed Edwards directly targeted the New York Democrat during an anti-war speech Sunday in Clinton's home turf.

In a speech last Sunday in Harlem, Edwards said, "If you're in Congress and you know that this war is going in the wrong direction . . . it is no longer OK to study your options and keep your own private counsel -- silence is betrayal. Speak out and stop this escalation now."

Top aide to Sen. Clinton Howard Wolfson took exception to Edwards' comments, telling the New York Post, "In 2004, John Edwards used to constantly brag about running a positive campaign. Today, he has unfortunately chosen to open his campaign with political attacks on Democrats who are fighting the Bush administration's Iraq policy."

Sen. Clinton has been a heavy critic of the president's war strategies, but she has not called for Congress to use the power of the purse to stop President Bush's plan to send more than 20,000 additional troops to Iraq, nor has she renounced her 2003 vote to authorize the war, which Edwards has done.

But Edwards denies that his comments were an attack on Clinton.

"I didn't speak about anybody by name," Edwards told CNN's Wolf Blitzer. "I talked about members of Congress. By the way, I also spoke to the American people who I think also need to step up and be heard on this escalation of the war."

"I believe I was right," Edwards added. "I stand behind it. We should not be escalating this war. And I hope that member of Congress will have the good conscience and the good sense to show strength."

Edwards, who declared he is making a second bid for the White House last month, also said he will attend New Hampshire's first presidential primary debate co-hosted by CNN, New Hampshire's WMUR-TV, and the New Hampshire Union Leader.