The tragedy happened at a birthday party in an apartment in Berkeley.
Five of the six young people who died were from the Republic of Ireland, and some of them were students at University College Dublin (UCD).
Counsellors are in place to help families and friends of the bereaved and injured. An Irish university has expressed “heartbreak” at the deaths.
Those who were killed have been named as:
Ashley Donohoe, 22
Olivia Burke, 21
Eoghan Culligan, 21
Niccolai Schuster, 21
Lorcan Miller, 21
Eimear Walsh, 21
Several others have been injured, some of them very seriously.
Ms Donohoe, who had dual US-Irish citizenship, lived in California while the other five who died all had home addresses in the Republic of Ireland.
Mr Culligan and Mr Schuster were both past pupils of St Mary’s College in Rathmines, Dublin.
The majority of the victims were in the US on work visas, as part of the J1 USA summer work and travel programme.
Irish Minister for Foreign Affairs Charlie Flanagan said his department was working closely with families who had arrived in the US and those preparing to travel.
“We are offering everything in terms of practical support to the bereaved families as they arrive in San Francisco,” he told RTÉ.
“The families will be met at the airport, we will provide transport, we will help in the arranging of accommodation and the setting up of appropriate meetings with the medical authorities for those who are injured and the coroners authorities for those who wish to see their loved ones.”
He said an emergency hotline received more than 500 calls from worried families, “which was testament to the widespread sense of anxiety right throughout the country”.
As an investigation gets under way, a number of factors are being looked at.
Kevin Moore, chairman of the structural standards committee of the Structural Engineers Association of California, said these include whether the balcony was built to code, if it was overloaded and if rain or other weather had weakened it.
Berkeley officials said the building code at the time of construction required the balcony to be able to hold at least 60 lbs per sq ft. That requirement has since been raised to 100 lbs.
Berkeley spokesman Matthai Chakko said officials had not measured the balcony to find out how big it was and how much weight it was built to bear based on the 60 lbs. per sq ft standard in place when the building went up.
Mr Chakko also said there was no city requirement to post a weight restriction for balconies in apartments.
UCD president Andrew Deeks expressed condolences to the victims’ families, saying: “We are heartbroken at their suffering and loss.”
In a statement, he said: “On behalf of the entire university community, I wish to extend our condolences to the families and friends of those who died and to those who were injured.
“We cannot comprehend the desperate shock and grief they are feeling.”
St Mary’s College paid tribute to its past pupils.
“The thoughts and prayers of everybody in the St Mary’s community are with the families of Niccolai and Eoghan, as well as the other Irish youngsters named by the US authorities this evening,” it said in a statement.
“We also pray particularly for those injured, and their families.”
Celine Kennelly of the Irish Immigration Pastoral Centre in California, said seven students were still in hospital and two of them were in a critical condition.
“Some have severe injuries, some are facing a long road ahead, some have undergone surgery today and others who are undergoing surgeries in the coming days,” she said.
“It’s a parent’s worst nightmare, it’s a community’s worst nightmare, it’s a country’s worst nightmare to hear of a tragedy like this and so many young lives taken.”
The Republic of Ireland’s Consul General in San Francisco Philip Grant said it had been a very traumatic time for everyone involved.
“To have this happen at the start of this season is something that has left us all frozen in shock and disbelief,” he said.
“It touches every single family in Ireland.”
Fr Aidan McAleenan from St Columba’s Church in Oakland near Berkeley, and who is originally from Banbridge, County Down, spent several hours with the injured and their friends.
“It was very emotional driving out and getting to the hospital and then having to tell some of them that another friend had died,” he told the BBC.
“It was really hard to know what to say or what to do. We prayed with them. Other people from the Irish community arrived – they are really devastated.”
US Ambassador to Ireland Kevin O’Malley said it was a “tragedy beyond belief”.
“We’ve never had an experience like this before and we’re terribly moved by it,” he said.
The national flag is being flown at half-mast at Irish government buildings as a mark of respect for those who died.
A book of condolence is being opened at the Mansion House in Dublin and in other cities in Ireland.
Lord Mayor of Dublin Christy Burke said it was a “very sad and tragic day”.
“The people of Dublin are strong and will support each other. I was in the city and people are just numb. Nobody can talk about it. It is a parent’s worst nightmare,” he said.