ZURICH (Reuters) - The Swiss government began untangling a legal mess on Wednesday over how to handle immigration from the European Union after parliament’s adoption of a law at odds with a constitutional amendment requiring quotas for EU citizens.

The new law, passed by parliament on Friday, gives local people first crack at open jobs, skirting voters’ demand in a 2014 referendum for outright quotas, which the government feared could disrupt close ties with the European Union.

Seeking to address the public’s concerns, the cabinet on Wednesday presented two options for anchoring voters’ wishes while preserving bilateral economic accords that include free movement of people - the price of Swiss access to the EU single market.

Both options, however, failed to offer the clear choice many Swiss had expected.

The first option would amend the constitution to make clear that when setting immigration policy Switzerland would take into account international treaties with far-reaching implications for the country’s role in Europe. These included bilateral accords which stipulate freedom of movement for EU citizens, and the European Convention on Human Rights.

The second option would remove the deadline for implementing immigration curbs voters embraced in 2014. This would leave open the possibility to amend free-movement rules in future.

Justice Minister Simonetta Sommaruga reiterated that the government wanted both stable ties with the EU and the ability to set immigration policy, and suggested the two options drawn up were the possible ways to square the policy circle.

Brussels has so far shown scant inclination to compromise on free movement of people - the principle underpinning Swiss access to the EU’s single market of 500 million - so as not to encourage Britain as it negotiates its EU divorce.

The Swiss cabinet aims to settle on one plan to send to parliament by late April, launching the process for another popular vote under the Swiss system of direct democracy.

Many Swiss had expected the government to offer a much clearer choice: curb immigration to Switzerland, whose population is already a quarter foreign, or declare flat out that Switzerland thinks preserving close EU ties is more important.

The government had said in October that voters deserved another say on the policy conundrum over ties with the EU, Switzerland’s biggest trading partner.

The proposals put forward on Wednesday add another moving part to the EU debate. A separate referendum campaign to overturn the 2014 vote completely is under way, and right-wing critics of the law passed last week have vowed to force a referendum on abrogating the free movement deal with the EU.