At a meeting of Schengen interior ministers in Brussels, Swiss Justice Minister Elisabeth Baume-Schneider said that only a third of migrants are being transferred to the relevant Dublin state.
She told the meeting on Thursday that this poor rate of transfers is weakening the credibility of the system.
The joint declaration, which was also signed by other countries including Germany, France and Austria, endorsed a roadmap set out last November.
The proposed new measures include screening and rapid asylum procedures at borders.
Ministers also agreed to the principle of a solidarity mechanism to relive the burden on countries that are particularly burdened by asylum seekers.
Baume-Schneider also wants all countries to coordinate visa policies for people from third countries to avoid too many visa exemptions.
The poor functioning of the system has led to rows between countries.
Switzerland has accused Italy of allowing asylum seekers to cross over the border too easily. Germany has made the same claim against Switzerland.
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Asylum cases increased in 2022, not counting Ukrainians
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Switzerland's State Secretariat for Migration (SEM) says it received 24,511 asylum applications in 2022, without counting Ukrainians.
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The large influx of refugees has filled accommodation centres to bursting point, obliging the Swiss authorities to distribute more asylum seekers to cantons.
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