The judge overseeing the case of a District man charged in the 2011 death of his socialite wife in their Georgetown home is determined to proceed with an October trial despite continued wrangling over the suspect’s mental health.

At a hearing Thursday in D.C. Superior Court, Judge Russell F. Canan urged prosecutors and attorneys for Albrecht G. Muth to continue work toward starting a trial on Oct. 9 as scheduled. Muth, 48, has been charged with first-degree murder in the Aug. 12, 2011, fatal beating of Viola Drath, 91.

“It seems to me that everyone should have an interest” in an October trial, Canan said.

Canan gave medical experts another 30 days to establish whether Muth is mentally competent to stand trial. Another hearing was scheduled for July 26.

Doctors at St. Elizabeths Hospital have been evaluating Muth for months and, in a recent letter, told the judge that they believe he is still incompetent.

In the letter, the doctors said that Muth — who has claimed to be a spy and a general in the Iraqi army — suffered from delusional and schizotypal personality disorders but would “likely” become competent eventually.

Prosecutors and defense attorneys agreed to the extension. But Muth’s defense attorney, Dana Page, said the extension likely would not allow for an October trial because one side or the other would challenge the conclusion of the St. Elizabeths doctors.

The defense would find it hard to proceed with the case “as long as [Muth] remains incompetent,” Page said.

Still, Canan urged attorneys for both sides to proceed with pre­trial discovery, the process by which prosecutors and defense attorneys obtain evidence from each other.

“I think we need to be pro­active here,” Canan said.

Muth was previously declared mentally incompetent to stand trial. At a hearing earlier this year, medical experts at St. Elizabeths said that Muth was making progress but requested — and were granted — more time to work with him.

The prosecution has retained two other medical experts to separately evaluate Muth’s mental health.

On Thursday, Muth spoke only to greet Canan.

“It seems to me you are making some progress in this journey here,” Canan told Muth before he dismissed the court.