Murphy spoke Friday after a meeting of the team's executive committee. He was not available for comment, but a team spokesman said the club president has "full confidence" in how Thompson and McCarthy are handling this matter.
Murphy's 83-year-old father died on Thursday morning in Florida, and a memorial service was scheduled for Monday in Clearwater, Fla.
Murphy was set to be in Florida this weekend and wouldn't attend the Packers Hall of Fame banquet set for Saturday.
Favre and his wife, Deanna, were expected to attend the event at the Lambeau Field Atrium.
Favre was to induct Frank Winters, a center who played for the Packers from 1992 to 2002.
The Packers have refused to release Favre. The three-time MVP said in March he was retiring but has since changed his mind.
Speaking on the Packers' statewide tour with fans last week, Murphy expressed support for Thompson and McCarthy regarding Favre.
"I've worked closely with Ted Thompson and Mike McCarthy on this, and they have my full support," Murphy said, according to the Green Bay Press-Gazette.
Although the Packers are publicly owned, the team's seven-member executive committee meets in private and doesn't publicize its agenda. The meetings generally cover all aspects of the team's operation and typically include a football report.
The team's annual shareholders meeting is planned for July 24 at Lambeau Field.
In an interview with The Associated Press this week, Pro Football Hall of Famer Willie Davis -- an emeritus member of the Packers' board of directors -- said Favre was bound to come up in any meeting involving high-level team executives.
"Obviously, right now, this is going to be a heavy discussion," Davis said.
A movement to summon fan support for Favre has fizzled so far. A rally in Green Bay drew fewer than 200 fans Sunday, and Monday's rally in the Milwaukee suburbs drew only 30 despite widespread local media attention. But shareholders supporting Favre still could call attention to the issue.
Shareholders, who elect the team's board of directors but don't directly control the team's day-to-day decision-making, aren't given the chance to ask questions during the meeting. But Murphy and Thompson will be there to mingle afterward.
Murphy, a former All-Pro safety for the Washington Redskins, got his law degree from Georgetown and worked as an assistant executive director of the NFL Players Association after his playing days. He took over for longtime Packers top executive Bob Harlan in January. Before joining the Packers, Murphy was the athletic director at Northwestern.
Unless he is released or traded, Favre's rights belong to the Packers until his current contract expires after the 2010 season.
Information from The Associated Press was used in this report.