Context :

Aims : Previous radio recombination line ( RRL ) observations of dust clumps identified in the APEX Telescope Large Area Survey of the Galaxy ( ATLASGAL ) have led to the detection of a large number of RRLs in the 3mm range .
Here , we aim to study their excitation with shorter wavelength ( sub ) millimeter radio recombination line ( submm-RRL ) observations .

Methods : We made observations of submm-RRLs with low principal quantum numbers ( n \leq 30 ) using the APEX 12 m telescope , toward 104 H ii regions associated with massive dust clumps from ATLASGAL .
The observations covered the H25 \alpha , H28 \alpha , and H35 \beta transitions .
Toward a small subsample the H26 \alpha , H27 \alpha , H29 \alpha , and H30 \alpha lines were observed to avoid contamination by molecular lines at adjacent frequencies .

Results : We have detected submm-RRLs ( signal-to-noise \geq 3 \sigma ) from compact H ii regions embedded within 93 clumps .
The submm-RRLs are approximately a factor of two brighter than the mm-RRLs and consistent with optically thin emission in local thermodynamic equilibrium ( LTE ) .
The average ratio ( 0.31 ) of the measured H35 \beta /H28 \alpha fluxes is close to the LTE value of 0.28 .
No indication of RRL maser emission has been found .
The Lyman photon flux , bolometric , and submm-RRL luminosities toward the submm-RRL detected sources present significant correlations .
The trends of dust temperature and the ratio of bolometric luminosity to clump mass , L _ { bol } / M _ { clump } , indicate that the H ii regions are related to the most massive and luminous clumps .
By estimating the production rate of ionizing photons , Q , from the submm-RRL flux , we find that the Q ( H28 \alpha ) measurements provide estimates of the Lyman continuum photon flux consistent with those determined from 5 GHz radio continuum emission .
Six RRL sources show line profiles that are a combination of a narrow and a broad Gaussian feature .
The broad features are likely associated with high-velocity ionized flows .

Conclusions : We have detected submm-RRLs toward 93 ATLASGAL clumps .
Six RRL sources have high-velocity RRL components likely driven by high-velocity ionized flows .
Their observed properties are consistent with thermal emission that correlates well with the Lyman continuum flux of the H ii regions .
The sample of H ii regions with mm/submm-RRL detections probes , in our Galaxy , luminous clumps ( L _ { bol } > 10 ^ { 4 } L _ { \odot } ) with high L _ { bol } / M _ { clump } .
We also provide suitable candidates for further studies of the morphology and kinematics of embedded , compact H ii regions with the Atacama Large Millimeter/submillimeter Array ( ALMA ) .