The consultation proposes extending PD rights for exploratory non-fracking shale gas development in England only, which would mean such schemes would not require planning permission.
In a statement, the Ministry of Housing, Communities and Local Government (MHCLG) said full hydraulic shale gas extraction "will remain subject to strict planning and environmental controls".
The consultation follows a written ministerial statement (WMS) issued in May, in which the government announced a range of measures aiming to speed up decision making on shale gas planning applications.
The document emphasises that any PD right would apply to exploratory and non-hydraulic fracturing operations only, and not operations that involve extraction or hydraulic fracturing.
The new right would exclude development requiring an environmental impact assessment, the document says, or development in Areas of Outstanding Natural Beauty, national parks, world heritage sites, sites of special scientific interest, scheduled monuments and conservation areas.
The MHCLG proposes that a prior approval process would be suitable for any PD right, suggesting that considerations "might include transport and highways impact, contamination issues, air quality and noise impacts, visual impacts, proximity of occupied areas, setting in the landscape, and could include an element of public consultation".
It goes on to say that the PD right should be temporary and apply for two years only.
The consultation document states: "The government remains fully committed to making planning decisions faster and fairer for all those affected by new development, and to ensure that local communities are fully involved in planning decisions that affect them."
PD rights "provide a simpler, more certain route to encourage development and speed up the planning system, and reduce the burden on developers and local planning authorities by removing the need for planning applications", it says.
The move to create a shale test drilling PD right "aims to support a decision-making regime that is fit for the future needs of the energy sector", the document adds.
The document adds that the MHCLG intends to publish new planning practice guidance on shale development once the revised National Planning Policy Framework has been launched, "ensuring clarity on issues such as cumulative impact, local plan making, and confirmation that planners can rely on the advice of regulatory experts".
The 14-week consultation ends on 25 October. The government said it will issue its response later in 2018.
The MHCLG said it will also consult in autumn 2018 on whether developers "should be required to undertake pre-application community engagement prior to submitting a planning application for shale gas development".
The WMS also promised a further consultation this summer "on the criteria required to trigger the inclusion of shale production projects into the Nationally Significant Infrastructure Projects regime".
In response to the proposals, Daniel Carey-Dawes, senior infrastructure campaigner at the Campaign to Protect Rural England, said: "If they press ahead with these proposals, the protests, outrage and anger from local people across the country will undoubtedly intensify.
"These proposals would be a complete perversion of the planning system and trample over the rights of local communities - all to fast-track an industry bringing environmental risks that would massively outweigh any suggested ‘benefit’ to our energy security."
The MHCLG consultation can be found here.