While Hagel and Dung knew of each other's service in Vietnam, they had never met.
Mr Hagel made the comments at a joint news conference with British Defence Secretary Philip Hammond.
The criticism came from both sides of the aisle, including from Nebraska Republican Chuck Hagel.
Senator CHUCK HAGEL (Republican, Nebraska): I don't see, Madame Secretary, how things are getting better.
Reflecting on his military service, Hagel said his time in the Army shaped him forever.
Mr Karzai has cancelled a scheduled press conference with visiting US Defence Secretary Chuck Hagel.
BBC: Hamid Karzai says US and Taliban sowing post-2014 fears
Hagel cautioned lawmakers about the difficulties surrounding any direct U.S. military action in Syria.
Instead, Defense Secretary Chuck Hagel has said Washington is reviewing its opposition to arming the opposition.
The Hagel-Martinez idea was to draw lines among the undocumented based on length of residence.
In no case was Mr. Hagel ever held to any kind of account for being wrong.
Hagel stopped briefly in Jordan Tuesday and ended his day in Riyadh, Saudi Arabia.
That portrayal was central to a failed campaign to derail Hagel's Senate confirmation in February.
On Wednesday, U.S. Secretary of Defense Chuck Hagel ordered up to 200 troops to Jordan.
CNN: Al-Assad to Western nations: Syrian rebels will turn on you
U.S. Defense Secretary Chuck Hagel said Washington is doing all it can to defuse the situation.
You would never guess that Chuck Hagel had been a Republican senator for 12 years.
But a Hagel candidacy could start a debate about Iraq inside the Republican party.
Chuck Hagel (R-NE), a potential presidential candidate, is offering a resolution opposing "escalation" of the war.
Confirming Hagel will send the message we want politicians to stand up for what they believe.
Mr. Hagel was expected to discuss the Wardak issue during Sunday's meeting with Mr. Karzai.
The White House said Mr. Hagel wouldn't comment, referring reporters to Mr. Obama's comments.
Republican leaders warned that Mr. Hagel would not have the 60 votes necessary to proceed.
Chuck Hagel has demonstrated afresh his contempt for the legislature by declining to do so.
Hagel III, John Seely Brown and Lang Davison in the Power of Pull.
What I can tell you is that Senator Hagel fought and bled for his country.
Confirmation hearings begin this week in the U.S. Senate for Defense Secretary-designate Chuck Hagel.
Chuck Hagel to become Secretary of Defense, as well as any vote on confirmation of Sen.
Democratic supporters of Hagel came to his defense this week as the vote drew near.
Or do you expect to see the same sort of resistance as Senator Hagel?
He believes that the Senate will confirm both Senator Hagel and John Brennan to those positions.
And I know that Senator Hagel looks forward to discussing that record with the Senate.
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