Police in Glasgow continued their search overnight for Cork student Karen Buckley, who has been missing since the early hours of Sunday, while earlier her parents made an emotional appeal for her safe return.

Detectives said they believe they found the 24-year-old's handbag in Dawsholm Park in the city this afternoon.

The search for Ms Buckley, who is from Mourneabbey near Mallow in north Cork, has now entered its fourth day.

The Glasgow Caledonian University student is training to become an occupational therapist. 

The parents of Ms Buckley made an emotional appeal for information at a news conference yesterday.

Her mother Marian Buckley said: "We just want Karen home safely, we are desperate. She's our only daughter, we love her dearly.

"If anybody has any information please come forward, we would dearly appreciate it."

Her father John added: "We love her to bits and we are devastated."

Karen Buckley's mother appeals for her safe return

Officers confirmed that a man they were seeking in relation to Ms Buckley's disappearance was assisting them with their inquiries and was not being treated as a suspect.

They said Ms Buckley went with this man to an apartment after leaving a nightclub at around 1am on Sunday and left that apartment at 4am on foot.

She had arrived at the Sanctuary club on Dumbarton Road with friends at around 11.45pm on Saturday.

At around 1am, she told them she was going to the toilet, but failed to return and did not take her jacket.

She was then seen on CCTV outside talking to a man and then walking westwards away from the city centre towards Church Street.

Police have also traced a second man who the student spoke to in the nightclub before she left.

Police are also keen to find out more about a grey car that was seen on the roads between Milngavie and Drymen north of Glasgow between 11am and 3pm yesterday.

Detective Superintendent Jim Kerr said: "The activity of this grey car on the Monday is something that we're a wee bit concerned about.

"This car has been seen at various locations on these roads and I want to know why.

"We are gravely concerned that Karen has come to some harm, whether that is down to foul play, criminality or she has taken unwell or had an accident is obviously still to be established."

Air and ground searches by police in the area, including in a park and along the River Kelvin, have been continuing.

Her friends raised the alarm on Sunday, saying it was "very out of character" for her not to return home.

A Facebook page - Please help find Karen missing in Glasgow - has been set up urging people to look for her.

Yesterday, Inspector Gavin Smith said: "Friends reported Karen missing on Sunday 12 April after feeling her behaviour to not return home was very out of character.

"Her friends say she would always contact them by text or phone to let them know where she was and she doesn't appear to have contacted anyone.

"We are interested in speaking to anyone who may have seen Karen in the early hours of Sunday morning in the west end of Glasgow in order to help with our inquiries to locate her.

"Karen had been drinking alcohol with her friends but they say she was not drunk and are very worried about her."

Ms Buckley lives with three other student friends in a flat on Hill Street in Garnethill, Glasgow.

She is described as being 1.52m to 1.58m (5ft to 5'2") tall with brown eyes and dark hair, which had long black curly extensions in it.

When last seen she was wearing a black jumpsuit with red high-heeled shoes and was carrying a black handbag.