Context. The diffuse interstellar bands (DIBs) are a set of hundreds of unidentified absorption features that appear almost ubiquitously throughout the interstellar medium. Most DIBs appear at optical wavelengths, but some are in the near-infrared.
Aims: We aim to characterise near-infrared DIBs at high spectral resolving power towards multiple targets.
Methods: We observed 76 early-type stars at a resolving power of 50 000 (velocity resolution ~6 km s−1) and signal-to-noise ratios of several hundreds using the CRyogenic high-resolution InfraRed Echelle Spectrograph (CRIRES). These data allow us to investigate the DIBs around 1318.1, 1527.4, 1561.1, 1565.1, 1567.0, 1574.4, and 1624.2 nm. We detected a total of six DIB features and 17 likely stellar features through comparisons with a model spectrum computed with CMFGEN. Additionally, we measured equivalent widths of the DIBs at 1318.1 and 1527.4 nm using observations with X-shooter towards ten very highly reddened (3.2 < E(B-V) < 6.5) Cepheid variable stars and towards four stars observed at low values of precipitable water vapour as well as by using other archive data.
Results: We measured correlations (correlation coefficient r ~ 0.73-0.96, depending on the subsample used) between DIB equivalent width and reddening for the DIBs at 1318.1, 1561.1, 1565.1, and 1567.0 nm. Comparing the near-infrared DIBs with 50 of the strongest optical DIBs, we find correlations r > ~0.8 between the 1318, 1527, 1561, 1565, and 1567 nm and the optical DIBs 5705, 5780, 6203, 6283, and 6269 Å. The 5797 Å DIB is less well correlated with the near-infrared DIBs. The DIB at 9632.1 Å, which is likely C60+, is not well correlated with the 1318.1 nm DIB. Partial correlation coefficients using E(B-V) as the covariate were also determined. For stars earlier than B2, the 1318.1 nm DIB is affected by an emission line on its blue wing that is likely stellar in nature, although we cannot rule out an interstellar or circumstellar origin for this line caused by, for example, a DIB in emission. The 1318.1 nm DIB also has an extended red wing. The line is reasonably well fitted by two Gaussian components, although neither the component equivalent width (EW) ratios nor the separation between components are obviously correlated with such indicators as λλ5780/5797 and reddening. The EW at 1318 nm correlates with H I with EW(1318 nm)/E(B - V) decreasing with f(H2). Five pairs of stars within one arcmin of each other show very similar 1318.1 nm DIB profiles. Possible variation in the 1318.1 nm feature is seen between HD 145501 and HD 145502 (separated by 41 arcsec, equivalent to 7200 au) and HD 168607 and HD 168625 (separated by 67 arcsec, equivalent to 0.52 pc on the plane of the sky). Seventeen sightlines have repeat CRIRES observations separated by six to 14 months, and two sightlines have repeat X-shooter observations separated by 9.9 yr. No time variability was detected in the 1318.1 nm DIB in the CRIRES data nor in the 5780.5 Å, 5797.1 Å, 1318.1 nm, and 1527.4 nm DIBs. Tentative time variation is observed in the C60+ DIBs at 9577 and 9632 Å towards HD 183143, although it is very close to the noise level and requires confirmation.
Conclusions: The Near Infrared (NIR) DIBs observed occur more in more UV-irradiated regions than the 5797 Å DIB allowing the study of heavily reddened sightlines. Future searches for time variability in DIBs will require either higher quality data, larger intervals between epochs, or both.

Equivalent width measurements of the measured lines (Table E.1) are only available at the CDS via anonymous ftp to cdsarc.cds.unistra.fr (ftp://130.79.128.5) or via https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/672/A181